A formal approach to queueing processes in the steady state and their applications
- 1 June 1979
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (2) , 332-346
- https://doi.org/10.2307/3212901
Abstract
Using the theory of point processes, we give a formal treatment to queueing processes in the steady state. Based on this result, we obtain invariance relations between several quantities in G/G/c queues. As applications, the finiteness of their moments is discussed for G/G′/c queues. The basic results and notations used in this paper are contained in the author's previous paper (Miyazawa (1977)).Keywords
This publication has 17 references indexed in Scilit:
- On the Theory of Queues with Many ServersPublished by Springer Nature ,1985
- Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneingMathematische Operationsforschung und Statistik. Series Optimization, 1978
- Existence, uniqueness and some in variance properties of stationary distributions for general single server queuesMathematische Operationsforschung und Statistik, 1976
- Einige Anwendungen der Theorie zufälliger Punktprozesse in der Bedienungstheorie IMathematische Nachrichten, 1975
- On two stationary distributions for the stable GI/G/1 queueJournal of Applied Probability, 1974
- A Generalization of L = λW to Moments of Queue Length and Waiting TimesOperations Research, 1972
- A relation between stationary queue and waiting time distributionsJournal of Applied Probability, 1971
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962
- On the Characteristics of the General Queueing Process, with Applications to Random WalkThe Annals of Mathematical Statistics, 1956
- Symmetric measures on Cartesian productsTransactions of the American Mathematical Society, 1955